The Relationship between Income Inequality and City Size: A General Equilibrium Model of an Open System of Cities Approach

A conclusion which emerges from studies of the factors affecting income inequality among cities is that many are connected through a number of different mechanisms with city size. The explanations are derived from partial equilibrium models of the labour market and ignore considerations associated with labour mobility among cities. To remedy this deficiency our paper employs a well developed general equilibrium model of an open system of cities to characterise the relationship between city size and income inequality that emerges. An outstanding conclusion derived is that, unlike existing explanations which provide justifications only for a unidirectional—positive or negative—rotation between city size and income inequality, the general equilibrium model applies no restrictions on the direction of the relation. Additional restrictions are therefore needed to justify a positive or negative relation. For instance, if households with high income have relative preferences for non-traded goods, whose prices are shown to rise with city size, while households with low income have relative preferences for traded goods, inequality will rise with city size. Conversely, if households with low income have relative preferences for non-traded goods while high-income households have relative preferences for traded goods, income inequality will decline with city size. The model is employed to derive a few propositions regarding the direction of the relation under diverse conditions. These propositions provide plausible explanations for certain relations which may prove to be useful for testing the relevancy of our model. The explanations are more flexible than previous explanations since they can cope with a wider range of predictions, including a reversal of the relation, compatible with empirical observations.